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Triangles on the Same Base (Or Equal Bases) and Equal Areas Will Lie between the Same Parallels

ΔABC is an eq...

Question

$Δ$ ABC is an equilateral triangle of side $2 \sqrt{3}$ cms, P is any point in the interior of $Δ$ ABC. If x, y, z are the distances of P from the sides of the triangle, then $x + y + z =$

2 + \sqrt{3}

cms

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5

cms

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3

cms

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4

cms

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Solution

The correct option is C $3$ cms
We have,
$A r (Δ A B C) = A r (Δ A O B + Δ A O C + Δ B O C)$
$\frac{(2 \sqrt{3})^{2} \sqrt{3}}{4} = \frac{1}{2} x \cdot 2 \sqrt{3} + \frac{1}{2} y \cdot 2 \sqrt{3} + \frac{1}{2} z \cdot 2 \sqrt{3}$
$\frac{12 \sqrt{3}}{4} = \frac{1}{2} 2 \sqrt{3} [x + y + z]$
$3 \sqrt{3} = \sqrt{3} [x + y + z]$
$3 = x + y + z$

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